"Stripe is building payment infrastructure for the Web, so we make it easy to accept credit cards online," its co-founder and president, John Collison, told CNBC. "Before Stripe, the way you'd do this is using the legacy banking structure. It was slow, it was complex, it was expensive. It had this very chilling effect on e-commerce."

Stripe is building out the product differently, he said. "Stripe does all the heavy lifting in the background and just gives the company the product they want to use."

With Stripe, any business can process transactions online, whether on a website or within a mobile application. While traditionally a business worked with a number of vendors to accept online payments, Stripe cuts out the middle, as well as the extra fees involved in dealing with multiple parties.

Other players are in this space, including PayPal, which is owned by eBay. But the market for online payment processing is growing so quickly that Stripe has major growth potential, Collison said on "Squawk Box."

"The market as a whole has grown," he said. "We're still seeing huge numbers of people come online, spending more time online. And what that means is people are getting more opportunity to realize value from the Internet, to get valuable services. So, yes, there's competition, but it's still a very rapidly growing market."

"Their main focus is this that ... commerce online is still a huge space with a lot of opportunity," Collison said. "So what we're focused on with Stripe is making it very easy for any business to start trading online and start accepting payment from customers."